Before somebody tells me there's something wrong with programs
LINE_ZIN and INPUT_Z I'd better put in a few words of explanation.

First of all there's nothing wrong with the programs. Both are
correct.

They both calculate the reflection coefficient Gamma for a given line
and given load impedance at a given frequency. One does it for coaxial
lines and the other for balanced-twin and open-wire lines.

But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

With program LINE_ZIN enter the following -

Freq = 0.2 MHz
Conductor diameter = 0.2 mm
Conductor spacing = 10 mm
Line length = 119.25 metres
Velocity factor = 1.00
Load resistance = 0.00 ohms
Load reactance = + 552.6 ohms

From which we get -

Zo = 552.6 ohms
Gamma = 1.084
Angle of Gamma = -90.0 degrees
SWR at load end = 24.8
SWR at input end = Infinity

With program INPUT_Z enter the following -

Frequ = 0.2 MHz
Zo = 50 ohms
Line length = 100 metres
Inner conductor diameter = 0.73 mm (RG-58)
Velocity factor = 0.66
Load resistance = 0.00 ohms
Load reactance = +50.00 ohms

From which we get -

Gamma = 1.109
Angle of Gamma = -90.0 degrees
SWR at load end = 19.3

The reason for the abnormally high values of Gamma, and the SWR at the
input end being higher than the SWR at the load end, is that the line
impedance Zo is not purely resistive. It has a negative angle. Zo =
Ro - jXo.

There is a resonance between -jXo and + jXload which causes the
reflected wave to be greater than the incident wave. Hence Gamma
exceeds unity. The effect is not present when jXload is negative.

Gamma has a maximum value when +Xload = Zo as can be found by varying
Xload on either side of Zo.

At some distance back from the load the extraordinary high value of
SWR occurs (as demonstrated with program LINE_ZIN) due to that point
taking the place of the end of the line when Zo is purely resistive.

The true value of Zo = Ro+jXo can be found by making the line long
enough such that attenuation exceeds about 35 or 40 dB. Line input
impedance is then becomes equal to Zo.

It is the fact that Zo is never purely resistive which causes errors
when using the Smith Chart. Errors which the user can be entirely
unaware of. Coax lines are more prone to error than higher impedance
balanced-twin lines.

The reason why both programs stop at 200 KHz has nothing to do with
the foregoing. It is due to skin effect not being fully operative at
lower frequencies which complicates calculations.
There are other programs which go down to audio and power frequencies.
----
Reg, G4FGQ

Reg Edwards wrote:
But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.
--
73, Cecil http://www.qsl.net/w5dxp

"Cecil Moore" wrote
That agrees with Chipman who says it only occurs in lossy lines.
============================================
Didn't you know ALL real lines are lossy?

Still, I'm pleased to hear Chipman agrees with me.
----
Reg.

On Sat, 08 Apr 2006 01:34:33 GMT, Cecil Moore
wrote:

Reg Edwards wrote:
But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.

But in theory, the line can have loss and this does not occur :-)

"Cecil Moore" wrote
That agrees with Chipman who says it only occurs in lossy lines.
============================================
Didn't you know ALL real lines are lossy?

Still, I'm pleased to hear Chipman agrees with me.
----
Reg.

=======================================

- - - - and perhaps I should add that I was well aquainted with the
behaviour of transmission lines well before Chipman wrote his book.
----
Reg.

On Sat, 8 Apr 2006 18:05:39 +0100, "Reg Edwards"
wrote:

- - - - and perhaps I should add that I was well aquainted with the
behaviour of transmission lines well before Chipman wrote his book.

Did you scribble it on the last page of Noah's log?

Reg Edwards wrote:
- - - - and perhaps I should add that I was well aquainted with the
behaviour of transmission lines well before Chipman wrote his book.

He wrote his book almost 40 years ago, Reg. Do you know
how old that makes you?
--
73, Cecil http://www.qsl.net/w5dxp

"Cecil Moore" wrote
Reg Edwards wrote:
- - - - and perhaps I should add that I was well aquainted with
the
behaviour of transmission lines well before Chipman wrote his
book.

He wrote his book almost 40 years ago, Reg. Do you know
how old that makes you?

=========================================

I may be in my 81st year but I DO know how old I am.

If Chipman wrote his book about 40 years ago then I was 40 years old
at the time. I have never written any books myself. I have never
attached sufficient importance to the subject matter. I educated
myself to enable me to do a job which was more interesting than merely
writing so-called bibles for a living.
----
Reg

Gamma Fans:

One area of practical interest for which Zo is not "real" occurs over
[broad] ranges is in the area of application of the so-called "last mile"
[for you Newbies that might be "first mile" (grin)] of POTS (Plain Old
Telephone Service) twisted pair transmission lines to a variety of
communications "last mile" communications systems.

Over the frequency ranges of interest for telephone cable applications i.e.
from below 25Hz or so for some signalling and on up to several hundred kHz
or even a few MHz for xDSL applications such as ISDN BA and HDSL, T1,
etc..., the telephone twisted pair exhibits a Zo that varies all over the
map!

In this arena, complex Zo and highly variable Gamma is the norm, in this
twisted pair media and for those kinds of applications, unfortunately for
Mr. Smith Zo is NOT purely resistive.

The Zo of twisted pair ranges rom very nearly purely capacitive impedance of
several thousand kOhms at low frequencies to purely resistive near 100 Ohms
at the higher ends.

Analysis and design of systems that operate over this 5-6 decade range of
frequencies must perforce use complex Zo!

Smith's venerable chart is completely useless. Smith's Chart is only for
"amateurs" who use transmission lines in very limited ways.

The complex reflection coeficient in all of its' glory reigns supreme for
those practical and realistic design and application scenarios.

Thoughts, comments?

--
Pete k1po
Indialantic, FL.


"Wes Stewart" wrote in message
...
On Sat, 08 Apr 2006 01:34:33 GMT, Cecil Moore
wrote:

Reg Edwards wrote:
But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.

But in theory, the line can have loss and this does not occur :-)

Peter O. Brackett wrote:

Gamma Fans:

One area of practical interest for which Zo is not "real" occurs over
[broad] ranges is in the area of application of the so-called "last mile"
[for you Newbies that might be "first mile" (grin)] of POTS (Plain Old
Telephone Service) twisted pair transmission lines to a variety of
communications "last mile" communications systems.

Over the frequency ranges of interest for telephone cable applications i.e.
from below 25Hz or so for some signalling and on up to several hundred kHz
or even a few MHz for xDSL applications such as ISDN BA and HDSL, T1,
etc..., the telephone twisted pair exhibits a Zo that varies all over the
map!

In this arena, complex Zo and highly variable Gamma is the norm, in this
twisted pair media and for those kinds of applications, unfortunately for
Mr. Smith Zo is NOT purely resistive.

The Zo of twisted pair ranges rom very nearly purely capacitive impedance of
several thousand kOhms at low frequencies to purely resistive near 100 Ohms
at the higher ends.

Analysis and design of systems that operate over this 5-6 decade range of
frequencies must perforce use complex Zo!

Smith's venerable chart is completely useless. Smith's Chart is only for
"amateurs" who use transmission lines in very limited ways.

The complex reflection coeficient in all of its' glory reigns supreme for
those practical and realistic design and application scenarios.

Thoughts, comments?

--
Pete k1po
Indialantic, FL.


"Wes Stewart" wrote in message
...

On Sat, 08 Apr 2006 01:34:33 GMT, Cecil Moore
wrote:


Reg Edwards wrote:

But, believe it or not, under certain load conditions the reflection
coefficient Gamma can exceed unity. Indeed, at a sufficiently low
frequency, Gamma can approach 1+Sqrt(2) = 2.414

That agrees with Chipman who says it only occurs in lossy lines.

But in theory, the line can have loss and this does not occur :-)





How are you, Peter? Is this some kind of religious controversy? I can't
imagine hams having any use for twisted pair transmission lines, but
maybe you can give your lines some fractal qualities, or show how
current can flow four directions at the same time in the same place in
them or the voltage at any given point on one of them must have 25
possible values simultaneously, or that the impedance on a typical line
is proportional to the square root of Cecil's forearm. In fact, giving
them any qualities that are impossible will endear them to
the great post hog on this newsgroup and start a never ending thread.
73,
Tom Donaly, KA6RUH